Call Libraries

library(tidyverse)
library(caret)
library(MASS)
library(car)
library(moments)

Calling the Transformed Datasets

income_cleaned = read_csv('NYS_Corp_Tax_Credit_data/income_cleaned.csv')
Rows: 1921 Columns: 6── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (2): Name, Group
dbl (4): Year, Num, Amount, Avg
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
income_cleaned
industry_cleaned = read_csv('NYS_Corp_Tax_Credit_data/industry_cleaned.csv')
Rows: 2476 Columns: 6── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (2): Name, Group
dbl (4): Year, Num, Amount, Avg
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
industry_cleaned

Creating the Models

income.model <- lm(sat.formula, data = income_cleaned)
Error in eval(predvars, data, env) : object 'Avg.bc' not found
# linear.model.cleaned2 <- lm(Avg ~ . - Amount, data = income_cleaned)
# s = summary(linear.model.cleaned)
# show(s)
# plot(linear.model.cleaned)
# 
# #histograms of response variable to check distribution
# hist(income_cleaned$Avg)
# hist(income_cleaned_bc$Avg.bc)
# 
# #Shapiro-Wilks test to evaluate normality
# shapiro.test(income_cleaned$Avg)
# shapiro.test(income_cleaned_bc$Avg.bc)
# 
# #Kurtosis evaluation (normal distribution has a value close to 3)
# moments::kurtosis(income_cleaned$Avg)
# moments::kurtosis(income_cleaned_bc$Avg.bc) #evaluated to 2.75 which means very close to 3 so it is normally distributed with possibly slightly less outliers. 

Correcting violation of Normality in previous model with BoxCox transform

Checking linear regression assumptions for the transformed data.

#Industry
sat.model.summary(industry_cleaned_bc, sat.field, sat.formula)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.9902, p-value = 5.826e-12

[1] 2.513097

Call:
lm(formula = sat.formula, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.2890 -0.4698  0.0171  0.4942  3.9076 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -6.143e+01  1.110e+01  -5.532 3.51e-08 ***
Year                                                                                           3.464e-02  5.504e-03   6.294 3.67e-10 ***
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                          2.667e-01  2.734e-01   0.976 0.329351    
NameAlternative Minimum Tax Credit                                                            -2.461e+00  2.273e-01 -10.827  < 2e-16 ***
NameBeer Production Credit                                                                     6.344e-01  3.381e-01   1.876 0.060762 .  
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  2.199e+00  2.416e-01   9.101  < 2e-16 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     2.726e+00  3.930e-01   6.937 5.13e-12 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.587e+00  2.581e-01   6.149 9.11e-10 ***
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              9.698e-01  2.571e-01   3.773 0.000165 ***
NameClean Heating Fuel Credit                                                                 -2.544e+00  2.482e-01 -10.250  < 2e-16 ***
NameConservation Easement Tax Credit                                                          -1.122e+00  2.538e-01  -4.421 1.03e-05 ***
NameCredit for Employment of Persons with Disabilities                                        -1.244e+00  2.738e-01  -4.546 5.74e-06 ***
NameCredit for Purchase of an Automated External Defibrillator                                -1.535e+00  2.411e-01  -6.364 2.34e-10 ***
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities     -8.142e-02  4.475e-01  -0.182 0.855647    
NameEmpire State Apprentice Tax Credit                                                        -8.684e-01  5.464e-01  -1.589 0.112126    
NameEmpire State Commercial Production Credit                                                  6.241e-01  3.333e-01   1.872 0.061269 .  
NameEmpire State Film Post Production Credit                                                   1.439e+00  2.821e-01   5.100 3.65e-07 ***
NameEmpire State Film Production Credit                                                        3.233e+00  2.584e-01  12.509  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                      1.012e+00  4.866e-01   2.080 0.037610 *  
NameExcelsior Jobs Program Credit                                                              1.644e+00  2.372e-01   6.930 5.39e-12 ***
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             1.310e+00  2.332e-01   5.619 2.14e-08 ***
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   7.150e-01  2.275e-01   3.142 0.001696 ** 
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.708e+00  2.264e-01   7.542 6.53e-14 ***
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           9.784e-01  2.328e-01   4.202 2.74e-05 ***
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                            1.616e-01  2.304e-01   0.701 0.483154    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    -5.234e-01  2.723e-01  -1.923 0.054647 .  
NameFarm Workforce Retention Credit                                                           -8.624e-01  2.890e-01  -2.984 0.002876 ** 
NameFarmers' School Tax Credit                                                                -1.158e+00  2.772e-01  -4.176 3.07e-05 ***
NameHire a Veteran Credit                                                                     -1.040e+00  4.457e-01  -2.333 0.019731 *  
NameHistoric Properties Rehabilitation Credit                                                  2.398e+00  2.614e-01   9.172  < 2e-16 ***
NameInvestment Tax Credit                                                                      6.997e-01  2.230e-01   3.138 0.001724 ** 
NameInvestment Tax Credit for the Financial Services Industry                                  1.561e+00  3.109e-01   5.020 5.53e-07 ***
NameLife Sciences Research & Development Tax Credit                                            9.053e-01  4.864e-01   1.861 0.062867 .  
NameLong-Term Care Insurance Credit                                                           -1.866e+00  2.268e-01  -8.228 3.08e-16 ***
NameLow-Income Housing Credit                                                                  1.331e+00  2.967e-01   4.486 7.58e-06 ***
NameManufacturer\u0092s Real Property Tax Credit                                              -6.077e-01  2.528e-01  -2.404 0.016286 *  
NameManufacturer�s Real Property Tax Credit                                                   -7.363e-01  2.758e-01  -2.669 0.007652 ** 
NameMinimum Wage Reimbursement Credit                                                         -9.159e-01  2.366e-01  -3.871 0.000111 ***
NameMortgage Servicing Tax Credit                                                              8.932e-01  3.490e-01   2.560 0.010540 *  
NameNew York Youth Jobs Program Tax Credit                                                     1.266e-01  2.307e-01   0.549 0.583231    
NameQETC Capital Tax Credit                                                                    1.163e+00  3.169e-01   3.670 0.000248 ***
NameQETC Employment Credit                                                                    -3.045e-01  2.412e-01  -1.263 0.206769    
NameQETC Facilities, Operations, and Training Credit                                           1.148e+00  3.624e-01   3.168 0.001554 ** 
NameSpecial Additional Mortgage Recording Tax Credit                                           7.509e-01  2.394e-01   3.137 0.001728 ** 
NameSTART-UP NY Tax Elimination Credit                                                        -1.834e+00  2.565e-01  -7.150 1.15e-12 ***
GroupAdministrative and Support and Waste Management and Remediation Services                  2.884e-01  1.360e-01   2.120 0.034078 *  
GroupAdministrative/Support/Waste Management/Remediation Services                              1.680e-01  1.511e-01   1.112 0.266251    
GroupAgriculture, Forestry, Fishing and Hunting                                               -1.135e-01  1.258e-01  -0.902 0.367038    
GroupArts, Entertainment, and Recreation                                                       5.595e-01  1.251e-01   4.472 8.11e-06 ***
GroupConstruction                                                                             -4.326e-02  1.172e-01  -0.369 0.712181    
GroupEducational Services                                                                      2.253e-01  1.592e-01   1.415 0.157097    
GroupFinance and Insurance                                                                     5.350e-01  1.099e-01   4.870 1.19e-06 ***
GroupHealth Care and Social Assistance                                                        -6.769e-02  1.237e-01  -0.547 0.584224    
GroupInformation                                                                               7.096e-01  1.176e-01   6.034 1.84e-09 ***
GroupManagement of Companies and Enterprises                                                   6.670e-01  1.053e-01   6.337 2.79e-10 ***
GroupManufacturing                                                                             4.604e-01  1.095e-01   4.204 2.72e-05 ***
GroupMining                                                                                    2.521e-01  1.940e-01   1.299 0.194080    
GroupMining, Quarrying, and Oil and Gas Extraction                                             3.858e-01  1.626e-01   2.372 0.017774 *  
GroupOther Services (except Public Administration)                                            -1.549e-01  1.197e-01  -1.293 0.195989    
GroupProfessional, Scientific, and Technical Services                                          4.877e-01  1.126e-01   4.332 1.54e-05 ***
GroupReal Estate and Rental and Leasing                                                        1.464e-01  1.104e-01   1.326 0.184896    
GroupRetail Trade                                                                              3.752e-01  1.100e-01   3.411 0.000657 ***
GroupTransportation and Warehousing                                                            2.125e-01  1.242e-01   1.711 0.087224 .  
GroupUtilities                                                                                 6.979e-01  1.422e-01   4.908 9.83e-07 ***
GroupWholesale Trade                                                                           4.364e-01  1.124e-01   3.882 0.000106 ***
Num                                                                                            4.555e-04  2.307e-04   1.974 0.048459 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8704 on 2410 degrees of freedom
Multiple R-squared:  0.7632,    Adjusted R-squared:  0.7568 
F-statistic: 119.5 on 65 and 2410 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.202893  1        1.484214
Name  5.218180 43        1.019397
Group 2.726612 20        1.025394
Num   1.371056  1        1.170921

Visualization and model stats

Stepwise Regression on Income_cat_bc (boxcox transformed dataset)

#creating dummy variable columns for stepwise
dummy_func <- function (df){
  x = model.matrix(Avg.bc ~., df)[, -1]
  dummy_bc = as.data.frame(x) %>% mutate(Avg.bc = df$Avg.bc)
  colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "-|'|/| |,|�" , '_')
  return(dummy_bc)
}

Cleaning column names further so stepwise regression doesn’t present any errors

summary(forwardBIC[['income']])$coefficients
                                                                                                   Estimate
(Intercept)                                                                                   -35.990882731
Group500_000_000___and_over                                                                     2.332162162
NameAlternative_Minimum_Tax_Credit                                                             -2.181442261
NameEmpire_State_Film_Production_Credit                                                         2.706498239
NameClean_Heating_Fuel_Credit                                                                  -3.225725322
NameLong_Term_Care_Insurance_Credit                                                            -3.009758493
NameCredit_for_Purchase_of_an_Automated_External_Defibrillator                                 -3.083797646
NameCredit_for_Employment_of_Persons_with_Disabilities                                         -3.263143617
Group100_000_000___499_999_999                                                                  1.687712446
NameIndustrial_or_Manufacturing_Business_Tax_Credit                                            -1.859343201
NameConservation_Easement_Tax_Credit                                                           -2.286344505
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_6_23_08_but_before_7_1_15   1.567464241
NameHistoric_Properties_Rehabilitation_Credit                                                   1.771621603
NameEZ_QEZE_Tax_Credits___EZ_Investment_Tax_Credit                                              0.743142678
NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes                                   1.075600313
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___Prior_to_6_23_08                        1.183854448
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_7_1_15                      2.528124751
Group50_000_000___99_999_999                                                                    1.471106534
Group25_000_000___49_999_999                                                                    1.323850513
Group1_000_000___24_999_999                                                                     1.102078605
NameEmpire_State_Film_Post_Production_Credit                                                    0.953736879
GroupZero_or_Net_Loss                                                                           1.009495036
NameSTART_UP_NY_Tax_Elimination_Credit                                                         -2.340948626
Num                                                                                            -0.001593991
NameNew_York_Youth_Jobs_Program_Tax_Credit                                                     -1.475123174
NameExcelsior_Jobs_Program_Credit                                                               0.319231772
NameHire_a_Veteran_Credit                                                                      -3.063449985
NameManufactureru0092s_Real_Property_Tax_Credit                                                -1.542240689
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit_For_Corporate_Partners                     -1.506419640
NameFarmers__School_Tax_Credit                                                                 -1.458275259
NameMinimum_Wage_Reimbursement_Credit                                                          -1.386166927
NameManufacturer_s_Real_Property_Tax_Credit                                                    -1.901589373
NameEmpire_State_Apprentice_Tax_Credit                                                         -2.354512875
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit                                            -0.994257922
NameFarm_Workforce_Retention_Credit                                                            -1.758773498
Group500_000___999_999                                                                          0.606172216
NameMortgage_Servicing_Tax_Credit                                                              -1.084274186
NameLow_Income_Housing_Credit                                                                  -1.053403737
Group100_000___499_999                                                                          0.362336938
NameQETC_Employment_Credit                                                                     -0.737161626
NameAlternative_Fuels_and_Electric_Vehicle_Recharging_Property_Credit                          -1.014111072
Year                                                                                            0.022774473
NameSpecial_Additional_Mortgage_Recording_Tax_Credit                                           -0.375077530
                                                                                                Std. Error
(Intercept)                                                                                   1.303392e+01
Group500_000_000___and_over                                                                   1.008232e-01
NameAlternative_Minimum_Tax_Credit                                                            1.329270e-01
NameEmpire_State_Film_Production_Credit                                                       1.611038e-01
NameClean_Heating_Fuel_Credit                                                                 1.730917e-01
NameLong_Term_Care_Insurance_Credit                                                           1.550110e-01
NameCredit_for_Purchase_of_an_Automated_External_Defibrillator                                1.492740e-01
NameCredit_for_Employment_of_Persons_with_Disabilities                                        2.075005e-01
Group100_000_000___499_999_999                                                                1.030520e-01
NameIndustrial_or_Manufacturing_Business_Tax_Credit                                           1.693476e-01
NameConservation_Easement_Tax_Credit                                                          1.892509e-01
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_6_23_08_but_before_7_1_15 1.610123e-01
NameHistoric_Properties_Rehabilitation_Credit                                                 1.863273e-01
NameEZ_QEZE_Tax_Credits___EZ_Investment_Tax_Credit                                            9.108533e-02
NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes                                 1.264744e-01
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___Prior_to_6_23_08                      1.592699e-01
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_7_1_15                    3.146055e-01
Group50_000_000___99_999_999                                                                  1.108276e-01
Group25_000_000___49_999_999                                                                  1.105266e-01
Group1_000_000___24_999_999                                                                   9.207831e-02
NameEmpire_State_Film_Post_Production_Credit                                                  1.836029e-01
GroupZero_or_Net_Loss                                                                         8.787141e-02
NameSTART_UP_NY_Tax_Elimination_Credit                                                        2.164849e-01
Num                                                                                           2.185414e-04
NameNew_York_Youth_Jobs_Program_Tax_Credit                                                    1.351498e-01
NameExcelsior_Jobs_Program_Credit                                                             1.428132e-01
NameHire_a_Veteran_Credit                                                                     4.216004e-01
NameManufactureru0092s_Real_Property_Tax_Credit                                               1.778721e-01
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit_For_Corporate_Partners                    1.801175e-01
NameFarmers__School_Tax_Credit                                                                1.722154e-01
NameMinimum_Wage_Reimbursement_Credit                                                         1.663310e-01
NameManufacturer_s_Real_Property_Tax_Credit                                                   2.490134e-01
NameEmpire_State_Apprentice_Tax_Credit                                                        3.468158e-01
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit                                           1.330842e-01
NameFarm_Workforce_Retention_Credit                                                           2.712498e-01
Group500_000___999_999                                                                        1.017994e-01
NameMortgage_Servicing_Tax_Credit                                                             1.987360e-01
NameLow_Income_Housing_Credit                                                                 2.086113e-01
Group100_000___499_999                                                                        9.429505e-02
NameQETC_Employment_Credit                                                                    1.742513e-01
NameAlternative_Fuels_and_Electric_Vehicle_Recharging_Property_Credit                         2.545435e-01
Year                                                                                          6.477265e-03
NameSpecial_Additional_Mortgage_Recording_Tax_Credit                                          1.275357e-01
                                                                                                 t value
(Intercept)                                                                                    -2.761325
Group500_000_000___and_over                                                                    23.131215
NameAlternative_Minimum_Tax_Credit                                                            -16.410833
NameEmpire_State_Film_Production_Credit                                                        16.799719
NameClean_Heating_Fuel_Credit                                                                 -18.635932
NameLong_Term_Care_Insurance_Credit                                                           -19.416413
NameCredit_for_Purchase_of_an_Automated_External_Defibrillator                                -20.658644
NameCredit_for_Employment_of_Persons_with_Disabilities                                        -15.725952
Group100_000_000___499_999_999                                                                 16.377290
NameIndustrial_or_Manufacturing_Business_Tax_Credit                                           -10.979445
NameConservation_Easement_Tax_Credit                                                          -12.081023
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_6_23_08_but_before_7_1_15   9.735059
NameHistoric_Properties_Rehabilitation_Credit                                                   9.508115
NameEZ_QEZE_Tax_Credits___EZ_Investment_Tax_Credit                                              8.158753
NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes                                   8.504488
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___Prior_to_6_23_08                        7.433007
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_7_1_15                      8.035858
Group50_000_000___99_999_999                                                                   13.273831
Group25_000_000___49_999_999                                                                   11.977660
Group1_000_000___24_999_999                                                                    11.968927
NameEmpire_State_Film_Post_Production_Credit                                                    5.194563
GroupZero_or_Net_Loss                                                                          11.488322
NameSTART_UP_NY_Tax_Elimination_Credit                                                        -10.813448
Num                                                                                            -7.293769
NameNew_York_Youth_Jobs_Program_Tax_Credit                                                    -10.914729
NameExcelsior_Jobs_Program_Credit                                                               2.235310
NameHire_a_Veteran_Credit                                                                      -7.266240
NameManufactureru0092s_Real_Property_Tax_Credit                                                -8.670503
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit_For_Corporate_Partners                     -8.363541
NameFarmers__School_Tax_Credit                                                                 -8.467739
NameMinimum_Wage_Reimbursement_Credit                                                          -8.333787
NameManufacturer_s_Real_Property_Tax_Credit                                                    -7.636495
NameEmpire_State_Apprentice_Tax_Credit                                                         -6.788943
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit                                            -7.470893
NameFarm_Workforce_Retention_Credit                                                            -6.483963
Group500_000___999_999                                                                          5.954577
NameMortgage_Servicing_Tax_Credit                                                              -5.455852
NameLow_Income_Housing_Credit                                                                  -5.049601
Group100_000___499_999                                                                          3.842587
NameQETC_Employment_Credit                                                                     -4.230451
NameAlternative_Fuels_and_Electric_Vehicle_Recharging_Property_Credit                          -3.984039
Year                                                                                            3.516063
NameSpecial_Additional_Mortgage_Recording_Tax_Credit                                           -2.940961
                                                                                                   Pr(>|t|)
(Intercept)                                                                                    5.812749e-03
Group500_000_000___and_over                                                                   2.297059e-104
NameAlternative_Minimum_Tax_Credit                                                             1.159347e-56
NameEmpire_State_Film_Production_Credit                                                        4.073941e-59
NameClean_Heating_Fuel_Credit                                                                  2.949876e-71
NameLong_Term_Care_Insurance_Credit                                                            1.117821e-76
NameCredit_for_Purchase_of_an_Automated_External_Defibrillator                                 1.322482e-85
NameCredit_for_Employment_of_Persons_with_Disabilities                                         1.913693e-52
Group100_000_000___499_999_999                                                                 1.878901e-56
NameIndustrial_or_Manufacturing_Business_Tax_Credit                                            3.165215e-27
NameConservation_Easement_Tax_Credit                                                           2.048552e-32
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_6_23_08_but_before_7_1_15  6.963935e-22
NameHistoric_Properties_Rehabilitation_Credit                                                  5.703747e-21
NameEZ_QEZE_Tax_Credits___EZ_Investment_Tax_Credit                                             6.128337e-16
NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes                                  3.664849e-17
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___Prior_to_6_23_08                       1.604289e-13
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_7_1_15                     1.625998e-15
Group50_000_000___99_999_999                                                                   1.681295e-38
Group25_000_000___49_999_999                                                                   6.549761e-32
Group1_000_000___24_999_999                                                                    7.222780e-32
NameEmpire_State_Film_Post_Production_Credit                                                   2.274726e-07
GroupZero_or_Net_Loss                                                                          1.432032e-29
NameSTART_UP_NY_Tax_Elimination_Credit                                                         1.759331e-26
Num                                                                                            4.423394e-13
NameNew_York_Youth_Jobs_Program_Tax_Credit                                                     6.194355e-27
NameExcelsior_Jobs_Program_Credit                                                              2.551416e-02
NameHire_a_Veteran_Credit                                                                      5.394423e-13
NameManufactureru0092s_Real_Property_Tax_Credit                                                9.129189e-18
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit_For_Corporate_Partners                     1.170266e-16
NameFarmers__School_Tax_Credit                                                                 4.968842e-17
NameMinimum_Wage_Reimbursement_Credit                                                          1.491953e-16
NameManufacturer_s_Real_Property_Tax_Credit                                                    3.531386e-14
NameEmpire_State_Apprentice_Tax_Credit                                                         1.509979e-11
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit                                            1.213726e-13
NameFarm_Workforce_Retention_Credit                                                            1.138968e-10
Group500_000___999_999                                                                         3.104646e-09
NameMortgage_Servicing_Tax_Credit                                                              5.519900e-08
NameLow_Income_Housing_Credit                                                                  4.855996e-07
Group100_000___499_999                                                                         1.257912e-04
NameQETC_Employment_Credit                                                                     2.444515e-05
NameAlternative_Fuels_and_Electric_Vehicle_Recharging_Property_Credit                          7.034072e-05
Year                                                                                           4.483930e-04
NameSpecial_Additional_Mortgage_Recording_Tax_Credit                                           3.311991e-03

Stepwise regression using BIC as the criteria (the penalty k = log(n)).

#checking our selected model's predictor variable's VIFs
vif(backwardBIC)
                                                                                         Year 
                                                                                     1.661856 
                        NameAlternative_Fuels_and_Electric_Vehicle_Recharging_Property_Credit 
                                                                                     1.040066 
                                                           NameAlternative_Minimum_Tax_Credit 
                                                                                     1.355727 
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_6_23_08_but_before_7_1_15 
                                                                                     1.077139 
                   NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_7_1_15 
                                                                                     1.032409 
                     NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___Prior_to_6_23_08 
                                                                                     1.076724 
                                                                NameClean_Heating_Fuel_Credit 
                                                                                     1.086361 
                                                         NameConservation_Easement_Tax_Credit 
                                                                                     1.071241 
                                       NameCredit_for_Employment_of_Persons_with_Disabilities 
                                                                                     1.050364 
                               NameCredit_for_Purchase_of_an_Automated_External_Defibrillator 
                                                                                     1.084252 
                                                       NameEmpire_State_Apprentice_Tax_Credit 
                                                                                     1.028286 
                                                 NameEmpire_State_Film_Post_Production_Credit 
                                                                                     1.067360 
                                                      NameEmpire_State_Film_Production_Credit 
                                                                                     1.079378 
                                           NameEZ_QEZE_Tax_Credits___EZ_Investment_Tax_Credit 
                                                                                     1.203345 
                                NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes 
                                                                                     1.110401 
                                          NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit 
                                                                                     1.094191 
                   NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit_For_Corporate_Partners 
                                                                                     1.059267 
                                                          NameFarm_Workforce_Retention_Credit 
                                                                                     1.043336 
                                                               NameFarmers__School_Tax_Credit 
                                                                                     1.075009 
                                                                    NameHire_a_Veteran_Credit 
                                                                                     1.016637 
                                                NameHistoric_Properties_Rehabilitation_Credit 
                                                                                     1.066991 
                                          NameIndustrial_or_Manufacturing_Business_Tax_Credit 
                                                                                     1.180919 
                                                          NameLong_Term_Care_Insurance_Credit 
                                                                                     1.085593 
                                                                NameLow_Income_Housing_Credit 
                                                                                     1.059690 
                                              NameManufactureru0092s_Real_Property_Tax_Credit 
                                                                                     1.059324 
                                                  NameManufacturer_s_Real_Property_Tax_Credit 
                                                                                     1.051337 
                                                        NameMinimum_Wage_Reimbursement_Credit 
                                                                                     1.074669 
                                                            NameMortgage_Servicing_Tax_Credit 
                                                                                     1.068997 
                                                   NameNew_York_Youth_Jobs_Program_Tax_Credit 
                                                                                     1.109900 
                                                                   NameQETC_Employment_Credit 
                                                                                     1.072612 
                                         NameSpecial_Additional_Mortgage_Recording_Tax_Credit 
                                                                                     1.114775 
                                                       NameSTART_UP_NY_Tax_Elimination_Credit 
                                                                                     1.055977 
                                                                    ENI1_000_000___24_999_999 
                                                                                     1.850053 
                                                                         ENI100_000___499_999 
                                                                                     1.795816 
                                                                 ENI100_000_000___499_999_999 
                                                                                     1.691776 
                                                                   ENI25_000_000___49_999_999 
                                                                                     1.578815 
                                                                   ENI50_000_000___99_999_999 
                                                                                     1.576866 
                                                                         ENI500_000___999_999 
                                                                                     1.708105 
                                                                    ENI500_000_000___and_over 
                                                                                     1.744570 
                                                                          ENIZero_or_Net_Loss 
                                                                                     1.867768 
                                                                                          Num 
                                                                                     1.533625 

Splitting data up into test data and training data (test data is for year 2019, training is the rest)

dim(X.test)
[1] 170  41

Lasso regression for comparison to backward stepwise

#create lambda grid
lambda.grid = 10^seq(2, -5, length = 100)

#create lasso models with lambda.grid
lasso.models = glmnet(X.train, y.train, alpha = 1, lambda = lambda.grid)

#visualize coefficient shrinkage
plot(lasso.models, xvar = "lambda", label = TRUE, main = "Lasso Regression")

#Cross Validation to find best lambda
set.seed(0)
cv.lasso.models <- cv.glmnet(X.train, y.train, alpha = 1, lambda = lambda.grid, nfolds = 10)

#visualize cross validation for lambda that minimizes the mean squared error.
plot(cv.lasso.models, main = "Lasso Regression")

#Checking the best lambda
log(cv.lasso.models$lambda.min)
best.lambda <- cv.lasso.models$lambda.min
best.lambda
# best lambda with all the variables was found to be 0.0006892612
# best lambda with only the bwdBIC coefficients included was found to be 0.0003053856

#looking at the lasso coefficients for the best.lambda
best.lambda.coeff <- predict(lasso.models, s = best.lambda, type = "coefficients")
best.lambda.coeff

#fitting a model with the best lambda found to be 0.000689 and using it to make predictions for the testing data.
lasso.best.lambda.train.pred <- predict(lasso.models, s = best.lambda, newx = X.test)
lasso.best.lambda.train.pred

#checking MSE
mean((lasso.best.lambda.train.pred - y.test)^2)
as.data.frame(lasso.best.lambda.train.pred) %>% mutate(Avg_in_dollars = (lasso.best.lambda.train.pred*lambda.bc+1)^(1/lambda.bc))
---
title: "R Notebook"
output: html_notebook
---
Call Libraries
```{r} 
library(tidyverse)
library(caret)
library(MASS)
library(car)
library(moments)
```


Calling the Transformed Datasets
```{r}
income_cleaned = read_csv('NYS_Corp_Tax_Credit_data/income_cleaned.csv')
income_cleaned
industry_cleaned = read_csv('NYS_Corp_Tax_Credit_data/industry_cleaned.csv')
industry_cleaned
```


Creating the Models
```{r}
sat.model.summary <- function (df, field, sat.formula){
    
    #Shapiro-Wilks test to evaluate normality
    print(shapiro.test(df[[field]]))
    
    #Kurtosis evaluation (normal distribution has a value close to 3)
    print(kurtosis(df[[field]]))
    linear.model.cleaned = lm(sat.formula, data = df)
    print(summary(linear.model.cleaned))
    plot(linear.model.cleaned)
    
    #histograms of response variable to check distribution
    print(df %>% 
      ggplot(aes_string(field)) + 
      geom_histogram() + 
      labs(title = 'Average Credit Amount Distribution') + 
      theme(plot.title = element_text(hjust = 0.5)))
    
    #Checking multicollinearity using VIF measurement
    print(vif(linear.model.cleaned))
    influencePlot(linear.model.cleaned)
    #avPlots(linear.model.cleaned)
}


sat.formula <- Avg ~ . - Amount
sat.field <- 'Avg'

sat.model.summary(income_cleaned, sat.field, sat.formula)
income.model <- lm(sat.formula, data = income_cleaned)

sat.model.summary(industry_cleaned, sat.field, sat.formula)
industry.model <- lm(sat.formula, data = industry_cleaned)
```

```{r}
# linear.model.cleaned2 <- lm(Avg ~ . - Amount, data = income_cleaned)
# s = summary(linear.model.cleaned)
# show(s)
# plot(linear.model.cleaned)
# 
# #histograms of response variable to check distribution
# hist(income_cleaned$Avg)
# hist(income_cleaned_bc$Avg.bc)
# 
# #Shapiro-Wilks test to evaluate normality
# shapiro.test(income_cleaned$Avg)
# shapiro.test(income_cleaned_bc$Avg.bc)
# 
# #Kurtosis evaluation (normal distribution has a value close to 3)
# moments::kurtosis(income_cleaned$Avg)
# moments::kurtosis(income_cleaned_bc$Avg.bc) #evaluated to 2.75 which means very close to 3 so it is normally distributed with possibly slightly less outliers. 
```

Correcting violation of Normality in previous model with BoxCox transform
```{r}
bc_func <- function (lm.cleaned, lambda.range){
  bc = boxCox(lm.cleaned, lambda = lambda.range)
  #Extracting the best lambda value.
  return(bc$x[which(bc$y == max(bc$y))])
}
  
#Income Group Dataset
income.lambda.bc = bc_func(income.model, seq(-0.2, 0.2, 1/10))

#Industry Group Dataset
industry.lambda.bc = bc_func(industry.model, seq(-0.2, 0.2, 1/10))
industry.lambda.bc

bc_transform <- function(df, lambda.bc){
  return (df %>% 
            mutate(Avg.bc = (Avg^lambda.bc -1)/lambda.bc) %>% 
            select(-c(Avg, Amount)))
}

sat.formula <- Avg.bc ~ .
sat.field <- 'Avg.bc'

#Income Group Dataset
income_cleaned_bc <- bc_transform(income_cleaned, income.lambda.bc)
income.model.bc = lm(Avg.bc ~ ., data = income_cleaned_bc)

#Industry Group Dataset
industry_cleaned_bc <- bc_transform(industry_cleaned, industry.lambda.bc)
industry.model.bc = lm(Avg.bc ~ ., data = industry_cleaned_bc)
```

Checking linear regression assumptions for the transformed data.
```{r}
#Income
sat.model.summary(income_cleaned_bc, sat.field, sat.formula)

#Industry
sat.model.summary(industry_cleaned_bc, sat.field, sat.formula)

```

Visualization and model stats
```{r}
BIC(income.model.bc, income.model)
BIC(industry.model.bc, industry.model)
```

Stepwise Regression on Income_cat_bc (boxcox transformed dataset)
```{r}
#creating dummy variable columns for stepwise
dummy_func <- function (df){
  x = model.matrix(Avg.bc ~., df)[, -1]
  dummy_bc = as.data.frame(x) %>% mutate(Avg.bc = df$Avg.bc)
  colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "-|'|/| |,|�" , '_')
  return(dummy_bc)
}
```

Cleaning column names further so stepwise regression doesn't present any errors
```{r}
#Income Group Dataset
income.dummy.bc <- dummy_func(income_cleaned_bc)
colnames(income.dummy.bc)[37] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(income.dummy.bc)

#Industry Group Dataset
industry.dummy.bc <- dummy_func(industry_cleaned_bc)
colnames(industry.dummy.bc)[35] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(industry.dummy.bc)

#creating models
bcs = list(income = income.dummy.bc, industry = industry.dummy.bc)
bcs[['industry']]
k = c('income', 'industry')
forwardBIC = list(income = NULL, industry = NULL)
forwardBIC[['income']]
backwardBIC = list(income = NULL, industry = NULL)

for (i in k){
  bc = bcs[[i]]
  model.empty = lm(Avg.bc ~ 1, data = bc) #intercept only
  model.full = lm(Avg.bc ~ ., data = bc) #All variables
  scope = list(lower = formula(model.empty), upper = formula(model.full))
  n_obs = bc %>% count() %>% first()
  forwardBIC[[i]] = step(model.empty, scope, direction = "forward", k = log(n_obs))
  backwardBIC[[i]] = step(model.full, scope, direction = "backward", k = log(n_obs))
}

for (i in k){
  fwd.BIC.summary.ENI <- data.frame(summary(forwardBIC)$coefficients)
  fwd.BIC.summary.ENI %>% arrange(rownames(fwd.BIC.summary.ENI)) #next time
}
summary(forwardBIC[['income']])$coefficients
```

Stepwise regression using BIC as the criteria (the penalty k = log(n)).
```{r}
#Forward BIC stepwise
forwardBIC = step(model.empty, scope, direction = "forward", k = log(n_obs))
fwd.BIC.summary.ENI <- data.frame(summary(forwardBIC)$coefficients)
fwd.BIC.summary.ENI %>% arrange(rownames(fwd.BIC.summary.ENI))

#Backward BIC stepwise
backwardBIC = step(model.full, scope, direction = "backward", k = log(n_obs))
bwd.BIC.summary.ENI <- data.frame(summary(backwardBIC)$coefficients)
bwd.BIC.summary.ENI %>% arrange(rownames(bwd.BIC.summary.ENI))

summary(forwardBIC)
summary(backwardBIC)

#inputing forwardBIC into a dataframe with index created as a column
fwd.BIC.summary.ENI$ENI = rownames(fwd.BIC.summary.ENI)
rownames(fwd.BIC.summary.ENI) = NULL
fwd.BIC.summary.ENI

#inputing backwardBIC into a dataframe with index created as a column
bwd.BIC.summary.ENI$ENI = rownames(bwd.BIC.summary.ENI)
rownames(bwd.BIC.summary.ENI) = NULL
bwd.BIC.summary.ENI

#comparing the forward and backward stepwise regression coefficients
anti_join(fwd.BIC.summary.ENI, bwd.BIC.summary.ENI, by = 'ENI')
inner_join(fwd.BIC.summary.ENI, bwd.BIC.summary.ENI, by = 'ENI')

#choosing backwardBIC because of negligible reduction in adjusted R^2 but we can reduce our sizable number of predictor variables.

#checking our selected model's predictor variable's VIFs
vif(backwardBIC)

best.formula <- backwardBIC$call[[2]]
```


Splitting data up into test data and training data (test data is for year 2019, training is the rest)
```{r}
data.test <- dummy_bc %>% filter(Year == 2019)
data.train <- dummy_bc %>% filter(Year != 2019)

#training model based on best.formula from stepwise
train.model <- lm(best.formula, data = data.train)
summary(train.model)

#train
#X.train <- as.matrix(data.train %>% select(-Avg.bc))
X.train <- model.matrix(best.formula, data = data.train)[,-1]
y.train <- as.matrix(data.train %>% select(Avg.bc))

#test
#X.test <- as.matrix(data.test %>% select(-Avg.bc))
X.test <- model.matrix(best.formula, data = data.test)[,-1]
y.test <- as.matrix(data.test %>% select(Avg.bc))

dim(X.train)
dim(X.test)
```


Lasso regression for comparison to backward stepwise
```{r}
#create lambda grid
lambda.grid = 10^seq(2, -5, length = 100)

#create lasso models with lambda.grid
lasso.models = glmnet(X.train, y.train, alpha = 1, lambda = lambda.grid)

#visualize coefficient shrinkage
plot(lasso.models, xvar = "lambda", label = TRUE, main = "Lasso Regression")

#Cross Validation to find best lambda
set.seed(0)
cv.lasso.models <- cv.glmnet(X.train, y.train, alpha = 1, lambda = lambda.grid, nfolds = 10)

#visualize cross validation for lambda that minimizes the mean squared error.
plot(cv.lasso.models, main = "Lasso Regression")

#Checking the best lambda
log(cv.lasso.models$lambda.min)
best.lambda <- cv.lasso.models$lambda.min
best.lambda
# best lambda with all the variables was found to be 0.0006892612
# best lambda with only the bwdBIC coefficients included was found to be 0.0003053856

#looking at the lasso coefficients for the best.lambda
best.lambda.coeff <- predict(lasso.models, s = best.lambda, type = "coefficients")
best.lambda.coeff

#fitting a model with the best lambda found to be 0.000689 and using it to make predictions for the testing data.
lasso.best.lambda.train.pred <- predict(lasso.models, s = best.lambda, newx = X.test)
lasso.best.lambda.train.pred

#checking MSE
mean((lasso.best.lambda.train.pred - y.test)^2)
```

```{r}
as.data.frame(lasso.best.lambda.train.pred) %>% mutate(Avg_in_dollars = (lasso.best.lambda.train.pred*lambda.bc+1)^(1/lambda.bc))
```

